Details

sample75.0ms

Algorithm

intervals

Results

40.0ms	101×	body	10240	exit
14.0ms	257×	body	80	valid
4.0ms	14×	body	640	valid
4.0ms	7×	body	1280	valid
1.0ms	9×	body	160	valid
0.0ms	3×	body	320	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.0b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
1.0b	(log (+ 1.0 (exp x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

48×	`prod-diff`
44×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
31×	`add-cube-cbrt`
19×	`pow1`
16×	`log-pow`
14×	`associate-l`
12×	`associate-r`
8×	`log-prod` `add-log-exp`
5×	`unswap-sqr`
4×	`add-exp-log` `log-div` `fma-neg` `associate--l+` `*-commutative` `distribute-lft-out--`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-` `diff-log` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 113

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
11.0ms	(- (log (+ 1.0 (exp x))) (* x y))
4.0ms	(log (+ 1.0 (exp x)))

series131.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
56.0ms	(- (log (+ 1.0 (exp x))) (* x y))
67.0ms	(log (+ 1.0 (exp x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	430	1368
1	1352	988
2	5001	966

prune202.0ms

Filtered

122 candidates to 61 candidates (50.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.7b

Counts

123 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
1.6b	(log (sqrt (+ 1.0 (exp x))))
1.6b	(log (sqrt (+ 1.0 (exp x))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

312×	`prod-diff`
300×	`log-pow`
264×	`*-un-lft-identity`
224×	`pow1`
213×	`add-sqr-sqrt`
156×	`add-cube-cbrt`
130×	`distribute-rgt-out`
117×	`distribute-lft-out`
83×	`associate-l`
80×	`sqrt-pow1` `pow1/2`
78×	`associate-r`
28×	`log-prod`
27×	`unswap-sqr`
26×	`distribute-lft1-in` `fma-neg` `distribute-rgt1-in` `*-commutative`
16×	`associate--l+` `sqrt-prod` `add-log-exp`
13×	`count-2`
10×	`distribute-lft-out--`
8×	`log-div` `sqrt-div`
7×	`associate-+l+` `associate-+r+`
6×	`add-exp-log`
5×	`flip3-+` `diff-log` `sum-log` `flip-+`
4×	`associate--l-` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`+-commutative` `associate-+l-` `associate-+r-` `rem-log-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `flip--`

Counts

4 → 449

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
39.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
153.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
105.0ms	(log (sqrt (+ 1.0 (exp x))))
108.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify124.0ms

Algorithm

egg-herbie

Counts

461 → 461

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	824	8109
1	2354	4947
2	5001	4704

prune611.0ms

Filtered

461 candidates to 109 candidates (23.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	460	1	461
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	460	4	464

Merged error: 0.7b

Counts

464 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
8.3b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

48×	`prod-diff`
43×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
30×	`add-cube-cbrt`
19×	`pow1`
16×	`log-pow`
14×	`associate-l`
12×	`associate-r`
6×	`log-prod` `add-log-exp`
5×	`unswap-sqr`
4×	`add-exp-log` `fma-neg` `*-commutative` `distribute-lft-out--`
3×	`expm1-log1p-u` `associate--l+` `add-cbrt-cube` `log1p-expm1-u`
2×	`diff-log` `difference-of-squares`
1×	`sub-neg` `flip3--` `rem-log-exp` `flip--` `fma-udef`

Counts

3 → 100

Calls

3 calls:

1.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
11.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series144.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
76.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
51.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	423	1473
1	1410	1074
2	5001	1050

prune191.0ms

Filtered

109 candidates to 52 candidates (47.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	109	4	113

Merged error: 0.7b

Counts

113 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (fma 1/2 (pow x 2) (+ x 2.0))))) (* x y))
0.7b	(log (sqrt (fma 1/2 (pow x 2) (+ x 2.0))))
1.6b	(log (sqrt (+ 1.0 (exp x))))
8.0b	(sqrt (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

129×	`*-un-lft-identity`
118×	`log-pow`
108×	`prod-diff`
95×	`pow1`
88×	`distribute-lft-out`
77×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
32×	`associate-l`
29×	`sqrt-pow1` `pow1/2`
27×	`associate-r`
26×	`log-prod`
17×	`sqrt-prod`
15×	`associate--l+`
14×	`add-log-exp`
10×	`distribute-lft-out--` `unswap-sqr`
9×	`fma-neg` `*-commutative`
7×	`associate-+l+`
6×	`add-exp-log` `associate-+r+`
5×	`diff-log`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `sum-log` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--l-` `associate-+l-` `flip3-+` `rem-log-exp` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `flip--`

Counts

4 → 220

Calls

4 calls:

28.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (fma 1/2 (pow x 2) (+ x 2.0))))) (* x y))
2.0ms	(log (sqrt (fma 1/2 (pow x 2) (+ x 2.0))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
2.0ms	(sqrt (fma 1/2 (pow x 2) (+ x 2.0)))

series696.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (fma 1/2 (pow x 2) (+ x 2.0))))) (* x y))
169.0ms	(log (sqrt (fma 1/2 (pow x 2) (+ x 2.0))))
102.0ms	(log (sqrt (+ 1.0 (exp x))))
75.0ms	(sqrt (fma 1/2 (pow x 2) (+ x 2.0)))

simplify110.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	755	4154
1	2604	3265
2	5002	3246

prune476.0ms

Filtered

232 candidates to 96 candidates (41.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	232	4	236

Merged error: 0.7b

Counts

236 → 4

regimes47.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms

sample1.7s

Algorithm

intervals

Results

985.0ms	2410×	body	10240	exit
314.0ms	8289×	body	80	valid
77.0ms	290×	body	640	valid
64.0ms	128×	body	1280	valid
29.0ms	182×	body	320	valid
8.0ms	87×	body	160	valid